Sample size, lag order and critical values of seasonal unit root tests

A response surface analysis for the distributions of popular tests for seasonal unit roots in quarterly observed time series variables is presented. Five test statistics are considered, along with the most commonly used specifications of the deterministic component in the test regression; allowance is also made for the lag order in the test regression to be determined endogenously, using commonly applied selection methods. Response surface coefficients are reported, permitting simple computation of accurate critical values for 1%-, 5%- and 10%-level tests and probability values for any sample size and lag order. Accurate approximations of the asymptotic distributions are obtained in the process of constructing the response surfaces. Dependence of the critical values and the probability density functions on the sample size and lag order is investigated.

[1]  P. Burridge,et al.  Bootstrapping the HEGY seasonal unit root tests , 2004 .

[2]  J. G. Cragg.  MORE EFFICIENT ESTIMATION IN THE PRESENCE OF HETEROSCEDASTICITY OF UNKNOWN FORM , 1983 .

[3]  James G. MacKinnon,et al.  Computing Numerical Distribution Functions in Econometrics , 2002 .

[4]  Byung Sam Yoo,et al.  Seasonal integration and cointegration , 1990 .

[5]  Distributions of Error Correction Tests for Cointegration , 1999 .

[6]  H. White,et al.  Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties☆ , 1985 .

[7]  D. Dickey.  Seasonal unit roots in aggregate U.S. data , 1993 .

[8]  Denise R. Osborn,et al.  The Econometric Analysis of Seasonal Time Series , 2001 .

[9]  Serena Ng,et al.  Unit Root Tests in ARMA Models with Data-Dependent Methods for the Selection of the Truncation Lag , 1995 .

[10]  Jeffrey A. Miron,et al.  Seasonal Unit Roots in Aggregate U.S. Data , 1992 .

[11]  P. Franses,et al.  Critical values for unit root tests in seasonal time series , 1997 .

[12]  Clive W. J. Granger,et al.  Long-Run Economic Relationships: Readings in Cointegration , 1991 .

[13]  James G. MacKinnon,et al.  Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration , 1996 .

[14]  David A. Dickey,et al.  Testing for Unit Roots in Seasonal Time Series , 1984 .

[15]  P. Sephton.  Response surface estimates of the KPSS stationarity test , 1995 .

[16]  Eric Ghysels,et al.  Testing for unit roots in seasonal time series: Some theoretical extensions and a Monte Carlo investigation , 1994 .

[17]  P. Burridge,et al.  On the Properties of Regression-Based Tests for Seasonal Unit Roots in the Presence of Higher-Order Serial Correlation , 2001 .

[18]  James G. MacKinnon,et al.  Critical Values for Cointegration Tests , 1990 .

[19]  Response surface estimates of stationarity tests with a structural break , 2003 .

[20]  James G. MacKinnon,et al.  Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests , 1994 .

[21]  Neil R. Ericsson.  Post-Stimulation Analysis of Monte Carlo Experiments : Interpreting Pesaran's (1974) Study of Non-Nested Hypothesis Test Statistics , 1986 .

[22]  Richard J. Smith,et al.  Additional critical values and asymptotic representations for seasonal unit root tests , 1998 .

[23]  Response surfaces estimates for the Dickey-Fuller unit root test with structural breaks , 1999 .

[24]  Ying-Wong Cheung,et al.  Lag Order and Critical Values of the Augmented Dickey-Fuller Test , 1995 .

[25]  James G. MacKinnon,et al.  Numerical Distribution Functions for Unit Root and Cointegration Tests , 1996 .